In conventional digital audio apparatus, such as a digital audio tape recorder (DAT) or compact disk (CD), audio data is encoded in accordance with the C1/C2 cross interleave product code. In more detail, audio data with a plurality symbols is first encoded in accordance with a second Reed-Solomon code (C2 code) capable of correcting triple errors, interleaved according to a predetermined order, and then encoded in accordance with a first Reed-Solomon code (C1 code) capable of correcting double errors.
In the conventional decoding system, a double-error correcting method or a quadruple-erasure correcting method is performed for decoding the data encoded based on the first Reed-Solomon code, a double-error correcting method or a sixfold-erasure correcting method are performed for decoding the data encoded based on the second Reed-Solomon code, under the constraint of real-time processing.
Here, an erasure is an erroneous symbol whose location is known. A symbol is a sequence of adjacent binary digits operated upon as a unit, and is the constitutional element of a word.
Conventional technologies related to this are disclosed in U.S. Pat. Nos. 4,476,562 assigned to Sony, and 4,875,211 assigned to Matsushita.
Referring to the Matsushita patent, the positions of two or more multiple-errors can be detected by a chain search algorithm. However, the calculation for the chain search algorithm must be repeatedly performed as many times as the number of symbols included in a word. On the other hand, in the Sony patent, a double-error correction and a quadruple-erasure correction can be easily performed, but a triple (or more) error correction cannot be performed.